Sorry this came out a lot longer than I wanted it to. Again!!!!!!
Counter steering works at all speeds. If you're moving at all its working. You are on round
tires so there is nothing to push off of to make the bike lean by shifting body weight without pushing the bike in the opposite direction. You probably could start to lean in one direction to very small extent on a very heavy motorcycle where the extra mass will resist being pushed around by a lighter rider or if you have a flat profile car tire on the rear. However, you would never be able to shift back to leaning the opposite way. For example if you start falling right just the slightest amount (I mean the smallest amount you could imagine) at 1mph you will inevitable continue falling right since your on round tires..... unless you counter steer. You can't be leaning right with gravity pulling you to the ground and suddenly decide to lean the opposite direction on round tires without some other force coming into play. Also thanks to the rake and trail a counter steer input automatically happens whether you make it or not at any speed. Without counter steering it would be completely impossible to ride at 1 or 2 mph but it can obviously be done.
Gyroscopic precession works because when you force a rotating mass off axis it tilts as well. In terms of a motorcycle if you tilt the axis (turn the handlebars) to the left on a horizontal plane, the gyroscopic force of the wheel will force the axle to tilt to the right on a vertical plane. So it literally leans the motorcycle by the forces moving through that narrow axle your wheel is spinning on. Its really easy to feel and see if you have a bicycle wheel. Hold it on each end of the axle, get the tire spinning, and try turning the axle left or right the same way a handlebar input would. Compared to the effect that inertia of the entire motorcycle has with counter steering the gyroscopic precession is a pretty small effect until some very high speeds. Its still not a necessary force to have at all to make counter steering work.
In terms of math, it would take the greatest minds in calculous months to figure out the formulas to get definitive numbers as to how much all of the 4 (or more) different factors make counter-steering work. Each of those factors are all changing constantly in effectiveness depending on the speed your traveling from 0.1mph all the way up to top speed. Some are more prominent at low speeds and have almost no effect at all when reaching higher speeds. So trying to "know" the physics behind it is a COMPLETE waste of time. Getting a basic understanding of how it works can help, but ultimately you just need to practice it. With how many people successfully ride motorcycles without knowing what counter steering is; you obviously don't need to understand the physics of how it works either! And for the record I never learned much calculous
If you want to see counter steering in action without the annoying complicated bullshit that a spinning tire causes you can just watch this in action. At 1:41 you can see a perfectly clear counter steer input in action with zero gyroscopic precession or any sort of static traction with a rolling tire on pavement. Its just a ski sliding on ice.